Squircles; New Shapes Using “Half-Angles”

When we were children, at a very early age, we learned about various shapes, and what they are called. Everyone knows that a three-sided shape is a triangle, four sides make a square, and seventeen sides and a third of a circle make a glifflomp. So, we are no stranger to shapes; that is for certain.

Shapes are somewhat concrete things; two dimensional objects, with an infinite amount of permutations, but we thought we had the nomenclature down pretty well; that all changed this week. Think squares have corners, and circles are lacking in them? Well, think again.

Okay, don’t think again. Those statements are still 100% correct, but now, thanks to the discovery of “Half-Angles,” there are several other possible shapes that we had never imagined before. We talked to geometer Vincent Rhombus about these new constructs:

“If you’re having trouble understanding what a “half-angle” is, just imagine this- Take an angle, and then make it not quite an angle. If you’re still having trouble, that’s okay; the human mind can’t actually comprehend these shapes. The instructions on how to imagine them were a joke.”

Some of the new, theoretical shapes that come from this are:

TRIANGURCLES: 3 sided, and also no sided; 3 half-angles

SQUIRCLES: 4 sided, and also no sided; 4 half-angles

GLIFFLIRCLES: 17 sides, 1/3 of a circle, also no sides and still 1/3 of a circle; unknown number of half-angles

When asked about the implications of this research, Rhombus said there weren’t any; he did mention that he enjoyed the sound of the names. In fact, some of the names are so soothing that they may be used to relax people before medical treatments. Certainly a triumph of geometry (and nomenclature).

(We would have liked to include a picture of at least one of the new shapes, but they are currently classified materials; half-angles could have implications in geometry-based weaponry, a growing global arms field.)